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A331372
Decimal expansion of Sum_{k>=1} 1/(2^k - 3).
2
3, 4, 3, 6, 7, 3, 4, 3, 3, 1, 8, 1, 7, 6, 9, 0, 1, 8, 5, 4, 4, 4, 8, 2, 8, 3, 3, 3, 8, 1, 2, 4, 1, 2, 0, 6, 1, 8, 8, 8, 0, 7, 1, 7, 6, 4, 8, 6, 7, 8, 3, 8, 4, 8, 6, 5, 1, 1, 0, 5, 9, 2, 1, 7, 4, 5, 5, 0, 0, 9, 5, 4, 1, 2, 4, 1, 8, 0, 9, 7, 4, 9, 5, 2, 6, 7, 8
OFFSET
0,1
COMMENTS
Erdős and Graham (1980) asked whether this constant is irrational, and Borwein (1991) proved that it is indeed irrational.
REFERENCES
Paul Erdős, Some of my favourite unsolved problems, in A. Baker, B. Bollobás and A. Hajnal (eds.), A tribute to Paul Erdős, Cambridge University Press, 1990, p. 470.
LINKS
Peter B. Borwein, On the irrationality of Sigma (1/(q^n + r)), Journal of Number Theory, Vol. 37, No. 3 (1991), pp. 253-259.
Paul Erdős and Ronald L. Graham, Old and new problems and results in combinatorial number theory, L'enseignement Mathématique, Université de Genève, 1980, p. 62.
EXAMPLE
0.34367343318176901854448283338124120618880717648678...
MATHEMATICA
RealDigits[Sum[1/(2^k - 3), {k, 1, 400}], 10, 100][[1]]
PROG
(PARI) suminf(k=1, 1/(2^k - 3)) \\ Michel Marcus, May 03 2020
CROSSREFS
Cf. A036563 (2^n-3), A065442.
Sequence in context: A117892 A286098 A074372 * A049276 A101684 A061800
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, May 03 2020
STATUS
approved